ABSTRACT
Numerical simulations of biological systems have become more and more important in recent years. In order to understand and predict hepatic function in health and disease, we developed a multiscale and multiphase model for the description of function-perfusion processes in the liver. With respect to the different scales of the hierarchically structured liver, processes like glucose homeostasis or detoxification of paracetamol as well as the influence of hepatic disease like the non-alcoholic fatty liver disease (NAFLD) can be investigated. On the tissue scale the liver consists of hexagonal liver lobules, containing anisotropically oriented capillaries, called sinusoids, which lead macroscopically to an anisotropic blood flow as well as a nonlinear, anisotropic and poro-elastic response. This structure is described using a homogenization method based on the Theory of Porous Media (TPM). This leads to a coupled set of partial differential equations (PDE) describing the tissue deformation as well as the transport of blood and metabolites like nutrients or xenobiotics. The lobule scale is coupled to the cellular scale where hepatic metabolism takes place. With the use of embedded ODE equations we can simulate metabolic processes depending on various nutrients or substances. The performance of the developed theory is demonstrated by a numerical example. The results provide an overview of possible applications of our approach using the NAFLD as a showcase. During the development of fatty liver, fat is stored in the liver cells resulting in swelling of the hepatocytes. This accumulation of fat drives tissue growth, which has an impact on the blood perfusion in the liver lobules. The results also clarify the spatial distribution of flow and fat accumulation since many hepatic processes proceed zonated. The processes in one single lobule are then expanded to a group of lobules to investigate the mutual liver lobe interaction.
